A note on Reeb dynamics on the tight 3-sphere

Frédéric Bourgeois; Kai Cieliebak; Tobias Ekholm

doi:10.3934/jmd.2007.1.597

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2007, Volume 1, Issue 4: 597-613. Doi: 10.3934/jmd.2007.1.597

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A note on Reeb dynamics on the tight 3-sphere

1.
Département de Mathématique, Université Libre de Bruxelles CP 218, Boulevard du Triomphe, 1050 Bruxelles
2.
Mathematisches Institut der LMU München, Theresienstr. 39, 80333 München
3.
Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala

Received: March 2007

Revised: July 2007

Published online: July 2007

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Abstract

We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. Moreover, in this case the Floquet multipliers and Conley-Zehnder indices of the two Reeb orbits agree with those of a suitable irrational ellipsoid in 4-space.

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Mathematics Subject Classification: Primary: 57R58; Secondary: 57R17, 35B10.

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